The Heat Equation + Special Announcement! | Infinite Series

What is the heat equation? And find out who the two new hosts of Infinite Series are!

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Hilbert's 15th Problem: Schubert Calculus | Infinite Series

Imagine a giant -- endless, infinite -- sheet of metal. For mathematical convenience, let’s overlay a grid. Now, imagine you light a very tiny and very powerful match directly underneath the origin, the point (0,0). This super special match instantaneously creates infinite heat at the origin, and zero heat everywhere else. Immediately remove the match and watch the heat diffuse along the surface, radiating out from the origin.

Links to Resources:
Distribution of Heat Graph

Normal Distribution Graph

3D Plot Heat Graph

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow

Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!

[pbsinfiniteseries]

Thank you all for making this such an amazing experience! Y'all are awesome!

Send me all your fun math things (especially if they're about the heat equation) on Twitter at @kelseyahe. I'm excited to join you all in the comment section here, and see what wild and beautiful mathematics Tai and Gabe are going to show us. -- Kelsey

[sebastianelytron]

"Before I say goodbye to you all"
*_Never says goodbye_*

[flymypg]

Thanks, Kelsey! Best of luck on your dissertation. I hope to eventually see videos from Dr. Houston-Edwards!

The Heat Equation has many applications outside thermodynamics. In electronics, for example, the charge distribution on a sheet of graphite. I'd also like to hear more about the equivalent discrete version, for example, the voltage applied to a grid of resistors.

Welcome back Gabe, and hello Tai-Danae! Can't wait to see what you share with us!

[ajayrawat]

I will miss you . You were an AMAZING host!

[shubhamshinde]

Sad to see kelsey go, but gabe's good i liked him on spacetime

[onepunchben]

GABE!! Man I missed you. It is crazy how the first PBS video I watched was your last. I'm so glad you are back.

[ericvilas]

Good luck, I wish you the best! We'll miss you!

[ugluwuglu]

You'll be missed. Good luck with your work!

[earfolds]

Thank you for your wonderful work on Infinite Series, Kelsey! Your personable comment sections at the end of each video in particular will be missed. You've made this show feel like an intimate get-together where we share the wonderful world of mathematics with each other. I wish you the best with your dissertation!

[fmnb]

Congratulations on your future! Your work really helped to launch the show.

[smijanic]

Happy to see Gabe is back, loved his fast talking videos.Makes you always wonder how many lines he just had before the show.

[codedragon]

This will be.... Hard. We won't forget you, ever. Hope to hear from you soon.

[jorgeluishita]

I have a PhD in Physics and I LOVE the way you explain this equation. With this reasoning it is easy to see why a solution of the heat equation can not oscillate in time. In this graph where the solution shows a "valley" and a "hill", at the moment that the values in the valley and the hill reach the equilibrium value, the solution stops evolving. Best luck with your dissertation! :-)

[nickg]

I'm a highschooler who was looking for this video for a project requiring that an object stay at a constant temperature. Sometimes doing research on your own is so much more fun than learning from others!

[Drachensslay]

Thank you for all of the amazing videos!

[danielribastandeitnik]

That video came right in time for me! I'm currently studing Fourier series as a solution to the heat equation! Nice explanation!

Thank you very much for hosting this show, I hope that all go well with your dissertation and that maybe you could come back in the future! Live long and prosper!

[michalchik]

I hope the new hosts watch most or all of the old episodes, to see how to do things right. For me I found this series to be a perfect balance of starting with the basics but not dumbing things down. I felt neither confused nor felt like my time was wasted

[MultivectorAnalysis]

Kelsey, it was so nice meeting you at the Joint Mathematics Meeting in Atlanta this past January. I'm very impressed (and grateful) that you managed to juggle being a PhD student and working on this outstanding youtube channel for so long! I totally understand your need to really focus now and finish your research. I do hope you return to making youtube educational content, as you have a real talent for it. Best of luck with the dissertation!

Regarding the new hosts, I'm excited that we'll have a mathematician and a physicist involved on this channel, and look forward to seeing where things go from here. I'm hoping at least one of you are familiar with Geometric Algebra (GA) and its associated multivector calculus (a.k.a. Clifford analysis), and would perhaps consider making an episode on it. GA is some truly beautiful mathematics with a fascinating history. If you're interested, you can check out the GA crash course I made on my channel.

[Tarnith]

Thanks for taking the time to make these videos, they've been excellent!

[fo-sho]

Good luck with your dissertation! Thank you soo much for starting this channel! Glad to see Gabe back!!! Can't wait for the new episodes!!!